1. Field of the Invention
The invention relates to the field of reflective dielectric structures, and more particularly to broadband reflective dielectric structures used as mirrors in laser systems.
2. Description of Related Art
Ultra short-pulse generation has advanced to a level where the bandwidth of standard Bragg mirrors, e.g. composed of TiO.sub.2 and SiO.sub.2 quarter-wave layers, limits the pulse width or tunability of the generated laser pulses. The limitation is two fold. First, due to the limited difference in refractive index of both materials, e.g., n.sub.TiO.sub..sub.2 .apprxeq.2.4 and n.sub.SiO.sub..sub.2 .apprxeq.1.45 the high reflectivity bandwidth of a standard quarter-wave Bragg mirror centered at 800 nm is only about 200 nm. Second, the higher order group delay dispersion (GDD) produced by quarter-wave Bragg mirrors further limits the useful bandwidth to about 100 nm which is just enough bandwidth for 10 fs pulses.
In a chirped mirror, the Bragg wavelength, .lambda..sub.B, of the individual layer pairs is varied from layer pair to layer pair (e.g. linearly), so that longer wavelengths penetrate deeper into the mirror structure than shorter wavelengths before being reflected. Such mirrors show an enlarged high reflectivity range and show a negative dispersion. However, the dispersion properties of these mirrors may be inadequate for ultra short pulse generation.
Chirped mirrors are also beneficial for the compression of high energy pulses, because they produce high dispersion with little material in the beam path, thereby avoiding nonlinear effects in the compressor. Thus, the design of these mirrors is extremely important for the further development of ultra fast laser sources.
It turns out that the design of a chirped mirror does not necessarily lead to a smooth and controlled GDD of the mirror. Using standard transfer matrix analysis of the multilayer structure as discussed in "Exact coupled mode theories for multilayer interference coating with arbitrary strong index modulations," IEEE J. Quant. Elec., vol. 33, March 1997, which is hereby incorporated by reference, one observes that the group delay produced by such a chirped mirror does not vary linearly with wavelength, as one would expect for a mirror with linearly chirped Bragg wavelength. The local average of the group delay shows the expected tendency to increase linearly with increasing wavelength. However, it also exhibits strong oscillations. The cause of these oscillations is the following. Longer wavelengths have to pass the first section of the Bragg mirror, which acts as a transmission grating for these wavelengths. The slight reflection in the front section interferes with the strong reflections from the deeper layers, as in a Gires-Toumouis Interferometer (GTI). The oscillations in the group delay have an amplitude of several tens of femtoseconds, which make these simple-chirped mirrors less useful for ultra short pulse generation.
What is needed is a mirror design which reduces the oscillations in the group delay, allowing control of the group delay dispersion while maintaining broad band reflectivity and low group delay dispersion.